Under what circumstances can I unlock the negative levels in Super Meat Boy?

Bandage girl has a random chance to glitch every time you spawn on a level. She can glitch in any level from 1 to 20 for each of the worlds 1 to 6, whether you're in the light or dark half of a world. There is exactly one negative level for every world.

To unlock level -1 for a world, pick a level in the world that is short and relatively easy. Below are good examples (in the light world) including a recommended character:

• 1-3 (The Gap) using anyone
• 2-10 (Johnny's Cage) using Jill (if you don't have Jill, see this video)
• 3-6 (The Shaft) using anyone
• 4-6 (Leviathan) using anyone
• 5-10 (Grinding Mill) using anyone
• 6-2 (Schism) using anyone

Then:

1. Look at or get to bandage girl and see if she is glitching. She will be spinning and making a distinctive pinging sound. I recommended levels where you can (mostly) see her from spawn.
2. If she is glitching then touch her to unlock level -1. Otherwise, kill yourself, respawn, and go back to step 1.
3. To play the level you just unlocked, go the light half of the world you unlocked it in. It will be available to play as a yellow-colored level beside level 1.

If you continuously die, Band-Aid Girl should eventually become glitched. While she is glitched, standing next to her should teleport you to the negative level. And you are correct, there are negative levels for Worlds 1 - 6.

Here is a video of somebody unlocking the first negative level.